Quadratic Functions Math

This topic covers - Solving quadratic equations - Graphing quadratic functions - Features of quadratic functions - Quadratic equationsfunctions word problems - Systems of quadratic equations - Quadratic inequalities

For an equation to be quadratic, the coefficient of x 2 will be a non-zero term a 0 Some examples of quadratic equations are x 2 2x - 15 0, here a 1, b 2, and c -15. x 2 - 49x 0, here a 1, b -49, and c 0. Sometimes the quadratic equations are outside the standard form and are disguised.

Quadratic function. A quadratic is a polynomial where the term with the highest power has a degree of 2. The parent function of quadratics is fx x 2. Quadratic functions follow the standard form fx ax 2 bx c. If ax 2 is not present, the function will be linear and not quadratic. Quadratic functions make a parabolic U-shape on a graph.

Section 2.5 Quadratic Equations - Part I. Before proceeding with this section we should note that the topic of solving quadratic equations will be covered in two sections. This is done for the benefit of those viewing the material on the web. This is a long topic and to keep page load times down to a minimum the material was split into two

Quadratic Equation in Standard Form ax 2 bx c 0 Quadratic Equations can be factored Quadratic Formula x b b 2 4ac 2a When the Discriminant b 2 4ac is positive, there are 2 real solutions zero, there is one real solution negative, there are 2 complex solutions

A quadratic function can be in different forms standard form, vertex form, and intercept form. Here are the general forms of each of them Standard form fx ax 2 bx c, where a 0. Vertex form fx ax - h 2 k, where a 0 and h, k is the vertex of the parabola representing the quadratic function. Intercept form fx ax - px - q, where a 0 and p, 0 and q, 0

Recognizing Characteristics of Parabolas. The graph of a quadratic function is a U-shaped curve called a parabola. One important feature of the graph is that it has an extreme point, called the vertex.If the parabola opens up, the vertex represents the lowest point on the graph, or the minimum value of the quadratic function. If the parabola opens down, the vertex represents the highest point

Understanding quadratic functions is a foundational step in mastering algebra and preparing for higher-level math. Their graphs provide visual insights into how variables change and interact. Whether you're a student or brushing up on math concepts, learning to graph and interpret quadratic functions will serve you well in academics and beyond.

All quadratic functions both increase and decrease. With a linear function, each input has an individual, unique output assuming the output is not a constant. With a quadratic function, pairs of unique independent variables will produce the same dependent variable, with only one exception the vertex for a given quadratic function.